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Direct Comparison

Direct Comparison problems involve simple inequality chains connecting multiple elements (e.g., A > B ≥ C > D). You must evaluate whether a given conclusion about two elements is definitely true, definitely false, or cannot be determined using the transitive property of inequalities.

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200+Practice Questions
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What You'll Learn

Introduction & Overview Why This Matters How to Solve Pro Tips & Tricks
Shortcut Methods Common Mistakes Practice Worksheets Exam Importance

Introduction to Direct Comparison

Direct Comparison problems involve simple inequality chains connecting multiple elements (e.g., A > B ≥ C > D). You must evaluate whether a given conclusion about two elements is definitely true, definitely false, or cannot be determined using the transitive property of inequalities.

Prerequisites

Understanding of inequality symbols (>, <, ≥, ≤, =) Knowledge of transitive property Basic logical reasoning Concept of 'cannot be determined' scenarios
Why This Matters: Direct Comparison is the most fundamental inequality problem type. You can expect 2-3 questions in SSC CGL, 2-3 in Banking PO, and 2-3 in Railways RRB exams.

How to Solve Direct Comparison Problems

1

Step 1: Identify all relationships between consecutive elements in the chain

2

Step 2: Determine if the chain has consistent direction (all >, all <, or mixed with =)

3

Step 3: For transitive conclusions, all intermediate signs must point the same direction

4

Step 4: If the path contains any reversal (e.g., > followed by <), no definite conclusion exists

5

Step 5: The '=' symbol preserves direction and can be included in any transitive chain

6

Step 6: If a conclusion is definitely true based on transitivity, mark it as True

7

Step 7: If a conclusion contradicts the given relationships, mark it as False

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Step 8: If multiple relationships are possible, answer 'Cannot be determined'

Pro Strategy: Always check the direction consistency along the entire path. If every step moves in the same direction (all 'greater than' or all 'less than', possibly with 'equal to'), transitivity applies. If any step reverses direction, no definite conclusion exists between the end points.

Example Problem

Example: Statement: A > B ≥ C > D. Conclusion: A > D. Is it true? Solution: Step 1: Chain: A > B, B ≥ C, C > D Step 2: All signs point from larger to smaller (consistent direction) Step 3: A > B and B ≥ C implies A > C (since A > B ≥ C means A > C) Step 4: A > C and C > D implies A > D Step 5: Therefore, A > D is definitely true Answer: True

Pro Tips & Tricks

  • Consistent > chain: A > B > C → A > C
  • Consistent < chain: A < B < C → A < C
  • Consistent ≥ chain: A ≥ B ≥ C → A ≥ C
  • Mixed signs: A > B < C → no definite relation between A and C
  • The '=' symbol preserves direction: A ≥ B = C → A ≥ C
  • If a conclusion uses a symbol not justified by the chain, it's likely false

Shortcut Methods to Solve Faster

For A > B > C, transitivity gives A > C
For A ≥ B ≥ C, transitivity gives A ≥ C
If A > B and B = C, then A > C
If A = B and B > C, then A > C
If the chain contains both > and <, outer elements have no definite relation

Common Mistakes to Avoid

Applying transitivity when signs point in opposite directions
Assuming 'cannot be determined' when a definite relationship exists
Forgetting that '≥' includes the possibility of equality
Misreading the direction of inequality symbols

Exam Importance

Direct Comparison is an important topic for various competitive exams. Here's how frequently it appears:

SSC CGL
2-3 questions
BANKING PO
2-3 questions
RAILWAYS RRB
2-3 questions
CAT
1-2 questions
GMAT
1-2 questions
INSURANCE
2-3 questions

Ready to Master Direct Comparison?

Start with Worksheet 1 and work your way up to expert level! Each worksheet includes:

20 practice questions
Detailed solutions
Step-by-step explanations
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